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4.1 Notes

# 4.1 Notes - 4.1 Solving systems of linear equations in two...

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4.1 Solving systems of linear equations in two variables Goal: Solve two equations with two unknowns Purpose: Find the break-even point where cost is equal to revenue Review: A solution of an equation in two variables is an ordered pair (x,y) that makes the equation true. An equation in two variables has an infinite number of solutions. A system of two equations in two variables is a pair of equations with the same two variables (two equations with two unknowns.) A solution of this system is an ordered pair (x,y) that makesboth equations true. This is the point where the graphs intersect. HW problem #1: Is (2, -1) a solution of the system? x – y = 3 2x – 4y = 8 Replacex with 2 and y with -1 in each equation:

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You can estimate the solution of a system of equations by graphing each equation. If the graphs are the same, the equations are dependent (infinite number of solutions) If the graphs are different, the equations are independent.
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